Marks: 60
The stock market has consistently proven to be a good place to invest in and save for the future. There are a lot of compelling reasons to invest in stocks. It can help in fighting inflation, create wealth, and also provides some tax benefits. Good steady returns on investments over a long period of time can also grow a lot more than seems possible. Also, thanks to the power of compound interest, the earlier one starts investing, the larger the corpus one can have for retirement. Overall, investing in stocks can help meet life's financial aspirations.
It is important to maintain a diversified portfolio when investing in stocks in order to maximise earnings under any market condition. Having a diversified portfolio tends to yield higher returns and face lower risk by tempering potential losses when the market is down. It is often easy to get lost in a sea of financial metrics to analyze while determining the worth of a stock, and doing the same for a multitude of stocks to identify the right picks for an individual can be a tedious task. By doing a cluster analysis, one can identify stocks that exhibit similar characteristics and ones which exhibit minimum correlation. This will help investors better analyze stocks across different market segments and help protect against risks that could make the portfolio vulnerable to losses.
Trade&Ahead is a financial consultancy firm who provide their customers with personalized investment strategies. They have hired you as a Data Scientist and provided you with data comprising stock price and some financial indicators for a few companies listed under the New York Stock Exchange. They have assigned you the tasks of analyzing the data, grouping the stocks based on the attributes provided, and sharing insights about the characteristics of each group.
# Libraries to help with reading and manipulating data
import numpy as np
import pandas as pd
# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_theme(style='darkgrid')
# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)
# to scale the data using z-score
from sklearn.preprocessing import StandardScaler
# to compute distances
from scipy.spatial.distance import cdist, pdist
# to perform k-means clustering and compute silhouette scores
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
# to visualize the elbow curve and silhouette scores
from yellowbrick.cluster import KElbowVisualizer, SilhouetteVisualizer
# to perform hierarchical clustering, compute cophenetic correlation, and create dendrograms
from sklearn.cluster import AgglomerativeClustering
from scipy.cluster.hierarchy import dendrogram, linkage, cophenet
# to suppress warnings
import warnings
warnings.filterwarnings("ignore")
data = pd.read_csv('stock_data.csv')
data.shape
rows, columns = data.shape
print(f"Number of rows: {rows}")
print(f"Number of columns: {columns}")
Number of rows: 340 Number of columns: 15
data.head()
| Ticker Symbol | Security | GICS Sector | GICS Sub Industry | Current Price | Price Change | Volatility | ROE | Cash Ratio | Net Cash Flow | Net Income | Earnings Per Share | Estimated Shares Outstanding | P/E Ratio | P/B Ratio | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | AAL | American Airlines Group | Industrials | Airlines | 42.349998 | 9.999995 | 1.687151 | 135 | 51 | -604000000 | 7610000000 | 11.39 | 6.681299e+08 | 3.718174 | -8.784219 |
| 1 | ABBV | AbbVie | Health Care | Pharmaceuticals | 59.240002 | 8.339433 | 2.197887 | 130 | 77 | 51000000 | 5144000000 | 3.15 | 1.633016e+09 | 18.806350 | -8.750068 |
| 2 | ABT | Abbott Laboratories | Health Care | Health Care Equipment | 44.910000 | 11.301121 | 1.273646 | 21 | 67 | 938000000 | 4423000000 | 2.94 | 1.504422e+09 | 15.275510 | -0.394171 |
| 3 | ADBE | Adobe Systems Inc | Information Technology | Application Software | 93.940002 | 13.977195 | 1.357679 | 9 | 180 | -240840000 | 629551000 | 1.26 | 4.996437e+08 | 74.555557 | 4.199651 |
| 4 | ADI | Analog Devices, Inc. | Information Technology | Semiconductors | 55.320000 | -1.827858 | 1.701169 | 14 | 272 | 315120000 | 696878000 | 0.31 | 2.247994e+09 | 178.451613 | 1.059810 |
data.sample(n=10, random_state=1)
| Ticker Symbol | Security | GICS Sector | GICS Sub Industry | Current Price | Price Change | Volatility | ROE | Cash Ratio | Net Cash Flow | Net Income | Earnings Per Share | Estimated Shares Outstanding | P/E Ratio | P/B Ratio | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 102 | DVN | Devon Energy Corp. | Energy | Oil & Gas Exploration & Production | 32.000000 | -15.478079 | 2.923698 | 205 | 70 | 830000000 | -14454000000 | -35.55 | 4.065823e+08 | 93.089287 | 1.785616 |
| 125 | FB | Information Technology | Internet Software & Services | 104.660004 | 16.224320 | 1.320606 | 8 | 958 | 592000000 | 3669000000 | 1.31 | 2.800763e+09 | 79.893133 | 5.884467 | |
| 11 | AIV | Apartment Investment & Mgmt | Real Estate | REITs | 40.029999 | 7.578608 | 1.163334 | 15 | 47 | 21818000 | 248710000 | 1.52 | 1.636250e+08 | 26.335526 | -1.269332 |
| 248 | PG | Procter & Gamble | Consumer Staples | Personal Products | 79.410004 | 10.660538 | 0.806056 | 17 | 129 | 160383000 | 636056000 | 3.28 | 4.913916e+08 | 24.070121 | -2.256747 |
| 238 | OXY | Occidental Petroleum | Energy | Oil & Gas Exploration & Production | 67.610001 | 0.865287 | 1.589520 | 32 | 64 | -588000000 | -7829000000 | -10.23 | 7.652981e+08 | 93.089287 | 3.345102 |
| 336 | YUM | Yum! Brands Inc | Consumer Discretionary | Restaurants | 52.516175 | -8.698917 | 1.478877 | 142 | 27 | 159000000 | 1293000000 | 2.97 | 4.353535e+08 | 17.682214 | -3.838260 |
| 112 | EQT | EQT Corporation | Energy | Oil & Gas Exploration & Production | 52.130001 | -21.253771 | 2.364883 | 2 | 201 | 523803000 | 85171000 | 0.56 | 1.520911e+08 | 93.089287 | 9.567952 |
| 147 | HAL | Halliburton Co. | Energy | Oil & Gas Equipment & Services | 34.040001 | -5.101751 | 1.966062 | 4 | 189 | 7786000000 | -671000000 | -0.79 | 8.493671e+08 | 93.089287 | 17.345857 |
| 89 | DFS | Discover Financial Services | Financials | Consumer Finance | 53.619999 | 3.653584 | 1.159897 | 20 | 99 | 2288000000 | 2297000000 | 5.14 | 4.468872e+08 | 10.431906 | -0.375934 |
| 173 | IVZ | Invesco Ltd. | Financials | Asset Management & Custody Banks | 33.480000 | 7.067477 | 1.580839 | 12 | 67 | 412000000 | 968100000 | 2.26 | 4.283628e+08 | 14.814159 | 4.218620 |
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 340 entries, 0 to 339 Data columns (total 15 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Ticker Symbol 340 non-null object 1 Security 340 non-null object 2 GICS Sector 340 non-null object 3 GICS Sub Industry 340 non-null object 4 Current Price 340 non-null float64 5 Price Change 340 non-null float64 6 Volatility 340 non-null float64 7 ROE 340 non-null int64 8 Cash Ratio 340 non-null int64 9 Net Cash Flow 340 non-null int64 10 Net Income 340 non-null int64 11 Earnings Per Share 340 non-null float64 12 Estimated Shares Outstanding 340 non-null float64 13 P/E Ratio 340 non-null float64 14 P/B Ratio 340 non-null float64 dtypes: float64(7), int64(4), object(4) memory usage: 40.0+ KB
df = data.copy()
df.duplicated().sum()
0
df.isna().sum()
Ticker Symbol 0 Security 0 GICS Sector 0 GICS Sub Industry 0 Current Price 0 Price Change 0 Volatility 0 ROE 0 Cash Ratio 0 Net Cash Flow 0 Net Income 0 Earnings Per Share 0 Estimated Shares Outstanding 0 P/E Ratio 0 P/B Ratio 0 dtype: int64
df.describe(include = 'all').T
| count | unique | top | freq | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Ticker Symbol | 340 | 340 | AAL | 1 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| Security | 340 | 340 | American Airlines Group | 1 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| GICS Sector | 340 | 11 | Industrials | 53 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| GICS Sub Industry | 340 | 104 | Oil & Gas Exploration & Production | 16 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| Current Price | 340.0 | NaN | NaN | NaN | 80.862345 | 98.055086 | 4.5 | 38.555 | 59.705 | 92.880001 | 1274.949951 |
| Price Change | 340.0 | NaN | NaN | NaN | 4.078194 | 12.006338 | -47.129693 | -0.939484 | 4.819505 | 10.695493 | 55.051683 |
| Volatility | 340.0 | NaN | NaN | NaN | 1.525976 | 0.591798 | 0.733163 | 1.134878 | 1.385593 | 1.695549 | 4.580042 |
| ROE | 340.0 | NaN | NaN | NaN | 39.597059 | 96.547538 | 1.0 | 9.75 | 15.0 | 27.0 | 917.0 |
| Cash Ratio | 340.0 | NaN | NaN | NaN | 70.023529 | 90.421331 | 0.0 | 18.0 | 47.0 | 99.0 | 958.0 |
| Net Cash Flow | 340.0 | NaN | NaN | NaN | 55537620.588235 | 1946365312.175789 | -11208000000.0 | -193906500.0 | 2098000.0 | 169810750.0 | 20764000000.0 |
| Net Income | 340.0 | NaN | NaN | NaN | 1494384602.941176 | 3940150279.327937 | -23528000000.0 | 352301250.0 | 707336000.0 | 1899000000.0 | 24442000000.0 |
| Earnings Per Share | 340.0 | NaN | NaN | NaN | 2.776662 | 6.587779 | -61.2 | 1.5575 | 2.895 | 4.62 | 50.09 |
| Estimated Shares Outstanding | 340.0 | NaN | NaN | NaN | 577028337.75403 | 845849595.417695 | 27672156.86 | 158848216.1 | 309675137.8 | 573117457.325 | 6159292035.0 |
| P/E Ratio | 340.0 | NaN | NaN | NaN | 32.612563 | 44.348731 | 2.935451 | 15.044653 | 20.819876 | 31.764755 | 528.039074 |
| P/B Ratio | 340.0 | NaN | NaN | NaN | -1.718249 | 13.966912 | -76.119077 | -4.352056 | -1.06717 | 3.917066 | 129.064585 |
#function to plot a boxplot and a histogram along the same scale.
def histogram_boxplot(df, feature, figsize=(12, 7), kde=False, bins=None):
"""
Boxplot and histogram combined
data: dataframe
feature: dataframe column
figsize: size of figure (default (12,7))
kde: whether to the show density curve (default False)
bins: number of bins for histogram (default None)
"""
f2, (ax_box2, ax_hist2) = plt.subplots(
nrows=2, # Number of rows of the subplot grid= 2
sharex=True, # x-axis will be shared among all subplots
gridspec_kw={"height_ratios": (0.25, 0.75)},
figsize=figsize,
) # creating the 2 subplots
sns.boxplot(
data=df, x=feature, ax=ax_box2, showmeans=True, color="violet"
) # boxplot will be created and a star will indicate the mean value of the column
sns.histplot(
data=df, x=feature, kde=kde, ax=ax_hist2, bins=bins, palette="winter"
) if bins else sns.histplot(
data=df, x=feature, kde=kde, ax=ax_hist2
) # For histogram
ax_hist2.axvline(
df[feature].mean(), color="green", linestyle="--"
) # Add mean to the histogram
ax_hist2.axvline(
df[feature].median(), color="black", linestyle="-"
) # Add median to the histogram
histogram_boxplot(df, 'Current Price')
histogram_boxplot(df, 'Price Change')
histogram_boxplot(df, 'Volatility')
Volatility has some outliers.
histogram_boxplot(df, 'ROE')
histogram_boxplot(df, 'Cash Ratio')
Cash ratio is positive and no negative that is good.
histogram_boxplot(df, 'Net Cash Flow')
histogram_boxplot(df, 'Net Income')
Mean of net income is positive
bhistogram_boxplot(df, 'Earnings Per Share')
Earnings per share has negative values and median is positive.
histogram_boxplot(df, 'Estimated Shares Outstanding')
histogram_boxplot(df, 'P/E Ratio')
histogram_boxplot(df, 'P/B Ratio')
# function to create labeled barplots
def labeled_barplot(df, feature, perc=False, n=None):
"""
Barplot with percentage at the top
data: dataframe
feature: dataframe column
perc: whether to display percentages instead of count (default is False)
n: displays the top n category levels (default is None, i.e., display all levels)
"""
total = len(df[feature]) # length of the column
count = df[feature].nunique()
if n is None:
plt.figure(figsize=(count + 1, 5))
else:
plt.figure(figsize=(n + 1, 5))
plt.xticks(rotation=90, fontsize=15)
ax = sns.countplot(
data=df,
x=feature,
palette="Paired",
order=df[feature].value_counts().index[:n].sort_values(),
)
for p in ax.patches:
if perc == True:
label = "{:.1f}%".format(
100 * p.get_height() / total
) # percentage of each class of the category
else:
label = p.get_height() # count of each level of the category
x = p.get_x() + p.get_width() / 2 # width of the plot
y = p.get_height() # height of the plot
ax.annotate(
label,
(x, y),
ha="center",
va="center",
size=12,
xytext=(0, 5),
textcoords="offset points",
) # annotate the percentage
plt.show() # show the plot
labeled_barplot(df, 'GICS Sector', perc=True)
labeled_barplot(df, 'GICS Sub Industry', perc=True)
1. What does the distribution of stock prices look like?
plt.figure(figsize=(15,8))
sns.barplot(data=df, x='Earnings Per Share', y='Current Price', ci=False)
plt.xticks(rotation=90)
plt.show()
2. The stocks of which economic sector have seen the maximum price increase on average?
plt.figure(figsize=(20,8))
sns.barplot(df, x='GICS Sector', y='Price Change')
#plt.xticks(rotation=90)
plt.show()
* Health care has maximum price increase follwed by consumer Staples.
* Energy is negative .
3. How are the different variables correlated with each other?
num_col = ['Current Price', 'Price Change', 'Volatility', 'ROE', 'Cash Ratio', 'Net Cash Flow', 'Net Income','Earnings Per Share','Estimated Shares Outstanding', 'P/E Ratio','P/B Ratio']
# correlation check
plt.figure(figsize=(15, 7))
sns.heatmap(
df[num_col].corr(), annot=True, vmin=-1, vmax=1, fmt=".2f", cmap="Spectral"
)
plt.show()
4. Cash ratio provides a measure of a company's ability to cover its short-term obligations using only cash and cash equivalents. How does the average cash ratio vary across economic sectors?
plt.figure(figsize=(20,8))
sns.barplot(df, x='GICS Sector', y='Cash Ratio')
#plt.xticks(rotation=90)
plt.show()
5. P/E ratios can help determine the relative value of a company's shares as they signify the amount of money an investor is willing to invest in a single share of a company per dollar of its earnings. How does the P/E ratio vary, on average, across economic sectors?
plt.figure(figsize=(20,8))
sns.barplot(df, x='GICS Sector', y='P/E Ratio')
#plt.xticks(rotation=90)
plt.show()
sns.pairplot(data=df[num_col], diag_kind="kde")
plt.show()
# Scaling the data set before clustering
scaler = StandardScaler()
subset = df[num_col].copy()
subset_scaled = scaler.fit_transform(subset)
#Creating a dataframe from the scaled data
subset_scaled_df = pd.DataFrame(subset_scaled, columns=subset.columns)
clusters = range(1, 15)
meanDistortions = []
for k in clusters:
model = KMeans(n_clusters=k)
model.fit(subset_scaled_df)
prediction = model.predict(subset_scaled_df)
distortion = (
sum(
np.min(cdist(subset_scaled_df, model.cluster_centers_, "euclidean"), axis=1)
)
/ subset_scaled_df.shape[0]
)
meanDistortions.append(distortion)
print("Number of Clusters:", k, "\tAverage Distortion:", distortion)
plt.plot(clusters, meanDistortions, "bx-")
plt.xlabel("k")
plt.ylabel("Average Distortion")
plt.title("Selecting k with the Elbow Method", fontsize=20)
Number of Clusters: 1 Average Distortion: 2.5425069919221697 Number of Clusters: 2 Average Distortion: 2.3832204631808573 Number of Clusters: 3 Average Distortion: 2.266134054458581 Number of Clusters: 4 Average Distortion: 2.178151429073042 Number of Clusters: 5 Average Distortion: 2.1225218310422096 Number of Clusters: 6 Average Distortion: 2.052570356366889 Number of Clusters: 7 Average Distortion: 2.0417691055838745 Number of Clusters: 8 Average Distortion: 1.9776786324440623 Number of Clusters: 9 Average Distortion: 1.941308387110628 Number of Clusters: 10 Average Distortion: 1.8929103751059646 Number of Clusters: 11 Average Distortion: 1.8092157318521074 Number of Clusters: 12 Average Distortion: 1.8226086368566154 Number of Clusters: 13 Average Distortion: 1.7434757429626366 Number of Clusters: 14 Average Distortion: 1.6657820296004255
Text(0.5, 1.0, 'Selecting k with the Elbow Method')
sil_score = []
cluster_list = list(range(2, 15))
for n_clusters in cluster_list:
clusterer = KMeans(n_clusters=n_clusters)
preds = clusterer.fit_predict((subset_scaled_df))
# centers = clusterer.cluster_centers_
score = silhouette_score(subset_scaled_df, preds)
sil_score.append(score)
print("For n_clusters = {}, silhouette score is {}".format(n_clusters, score))
plt.plot(cluster_list, sil_score)
For n_clusters = 2, silhouette score is 0.43969639509980457 For n_clusters = 3, silhouette score is 0.4644405674779404 For n_clusters = 4, silhouette score is 0.4592363230636684 For n_clusters = 5, silhouette score is 0.4200700306792197 For n_clusters = 6, silhouette score is 0.3407278364144909 For n_clusters = 7, silhouette score is 0.4020029196996943 For n_clusters = 8, silhouette score is 0.365306590903461 For n_clusters = 9, silhouette score is 0.387023345347161 For n_clusters = 10, silhouette score is 0.1583824436117129 For n_clusters = 11, silhouette score is 0.1428954892042367 For n_clusters = 12, silhouette score is 0.16434245610958667 For n_clusters = 13, silhouette score is 0.1485206015176479 For n_clusters = 14, silhouette score is 0.14916816514998216
[<matplotlib.lines.Line2D at 0x27678116e10>]
# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(3, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()
<Axes: title={'center': 'Silhouette Plot of KMeans Clustering for 340 Samples in 3 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>
# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(4, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()
<Axes: title={'center': 'Silhouette Plot of KMeans Clustering for 340 Samples in 4 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>
# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(5, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()
<Axes: title={'center': 'Silhouette Plot of KMeans Clustering for 340 Samples in 5 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>
# finding optimal no. of clusters with silhouette coefficients
visualizer = SilhouetteVisualizer(KMeans(2, random_state=1))
visualizer.fit(subset_scaled_df)
visualizer.show()
<Axes: title={'center': 'Silhouette Plot of KMeans Clustering for 340 Samples in 2 Centers'}, xlabel='silhouette coefficient values', ylabel='cluster label'>
# let's take 3 as number of clusters
kmeans = KMeans(n_clusters=6, random_state=0)
kmeans.fit(subset_scaled_df)
KMeans(n_clusters=6, random_state=0)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
KMeans(n_clusters=6, random_state=0)
# adding kmeans cluster labels to the original dataframe
df["K_means_segments"] = kmeans.labels_
km_cluster_profile = df.groupby("K_means_segments").mean(numeric_only=True)
km_cluster_profile["count_in_each_segment"] = (
df.groupby("K_means_segments")["Security"].count().values
)
# let's display cluster profiles
km_cluster_profile.style.highlight_max(color="lightgreen", axis=0)
| Current Price | Price Change | Volatility | ROE | Cash Ratio | Net Cash Flow | Net Income | Earnings Per Share | Estimated Shares Outstanding | P/E Ratio | P/B Ratio | count_in_each_segment | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| K_means_segments | ||||||||||||
| 0 | 71.950876 | 5.044297 | 1.376341 | 24.981273 | 51.393258 | 86249048.689139 | 1564498996.254682 | 3.698333 | 436647493.695543 | 23.420260 | -3.270855 | 267 |
| 1 | 50.517273 | 5.747586 | 1.130399 | 31.090909 | 75.909091 | -1072272727.272727 | 14833090909.090910 | 4.154545 | 4298826628.727273 | 14.803577 | -4.552119 | 11 |
| 2 | 26.990000 | -14.060688 | 3.296307 | 603.000000 | 57.333333 | -585000000.000000 | -17555666666.666668 | -39.726667 | 481910081.666667 | 71.528835 | 1.638633 | 3 |
| 3 | 108.304002 | 10.737770 | 1.165694 | 566.200000 | 26.600000 | -278760000.000000 | 687180000.000000 | 1.548000 | 349607057.720000 | 34.898915 | -16.851358 | 5 |
| 4 | 214.537220 | 12.970653 | 1.770434 | 28.833333 | 291.041667 | 206160166.666667 | 1115363083.333333 | 6.433333 | 532903567.855000 | 36.603080 | 15.658454 | 24 |
| 5 | 65.174668 | -11.542247 | 2.690220 | 37.300000 | 65.366667 | 195008366.666667 | -1677736033.333333 | -4.401667 | 544473664.718000 | 113.488924 | 1.424161 | 30 |
## code to print the companies in each cluster
for cl in df["GICS Sector"].unique():
print("In cluster {}, the following companies are present:".format(cl))
print(df[df["GICS Sector"] == cl]["Security"].unique())
print()
In cluster Industrials, the following companies are present: ['American Airlines Group' 'Alaska Air Group Inc' 'Allegion' 'AMETEK Inc' 'Arconic Inc' 'Boeing Company' 'Caterpillar Inc.' 'C. H. Robinson Worldwide' 'Cummins Inc.' 'CSX Corp.' 'Delta Air Lines' 'Deere & Co.' 'Danaher Corp.' 'Dun & Bradstreet' 'Dover Corp.' 'Equifax Inc.' 'Eaton Corporation' "Expeditors Int'l" 'Fastenal Co' 'Fortune Brands Home & Security' 'Fluor Corp.' 'Flowserve Corporation' 'General Dynamics' 'Grainger (W.W.) Inc.' "Honeywell Int'l Inc." 'Illinois Tool Works' 'J. B. Hunt Transport Services' 'Jacobs Engineering Group' 'Kansas City Southern' 'Leggett & Platt' 'L-3 Communications Holdings' 'Lockheed Martin Corp.' 'Southwest Airlines' 'Masco Corp.' '3M Company' 'Nielsen Holdings' 'Norfolk Southern Corp.' 'Pitney-Bowes' 'PACCAR Inc.' 'Pentair Ltd.' 'Quanta Services Inc.' 'Ryder System' 'Robert Half International' 'Roper Industries' 'Republic Services Inc' 'Stericycle Inc' 'United Continental Holdings' 'Union Pacific' 'United Parcel Service' 'United Technologies' 'Verisk Analytics' 'Waste Management Inc.' 'Xylem Inc.'] In cluster Health Care, the following companies are present: ['AbbVie' 'Abbott Laboratories' 'Alexion Pharmaceuticals' 'Amgen Inc' 'Anthem Inc.' 'Baxter International Inc.' 'Bard (C.R.) Inc.' 'BIOGEN IDEC Inc.' 'Bristol-Myers Squibb' 'Boston Scientific' 'Celgene Corp.' 'CIGNA Corp.' 'Centene Corporation' 'The Cooper Companies' 'Quest Diagnostics' 'DaVita Inc.' 'Edwards Lifesciences' 'Gilead Sciences' 'HCA Holdings' 'Henry Schein' 'Humana Inc.' 'IDEXX Laboratories' 'Intuitive Surgical Inc.' 'Laboratory Corp. of America Holding' 'Lilly (Eli) & Co.' 'Merck & Co.' 'Mettler Toledo' 'Mylan N.V.' 'Pfizer Inc.' 'Regeneron' 'Stryker Corp.' 'Thermo Fisher Scientific' 'Universal Health Services, Inc.' 'United Health Group Inc.' 'Varian Medical Systems' 'Vertex Pharmaceuticals Inc' 'Waters Corporation' 'Dentsply Sirona' 'Zimmer Biomet Holdings' 'Zoetis'] In cluster Information Technology, the following companies are present: ['Adobe Systems Inc' 'Analog Devices, Inc.' 'Alliance Data Systems' 'Akamai Technologies Inc' 'Applied Materials Inc' 'Amphenol Corp' 'Activision Blizzard' 'Broadcom' 'Cognizant Technology Solutions' 'Citrix Systems' 'eBay Inc.' 'Facebook' 'Fidelity National Information Services' 'Fiserv Inc' 'FLIR Systems' 'First Solar Inc' 'Corning Inc.' 'Hewlett Packard Enterprise' 'HP Inc.' 'International Business Machines' 'Intel Corp.' 'Juniper Networks' 'Mastercard Inc.' 'Netflix Inc.' 'PayPal' 'Skyworks Solutions' 'Teradata Corp.' 'Total System Services' 'Texas Instruments' 'Verisign Inc.' 'Western Union Co' 'Xerox Corp.' 'Yahoo Inc.'] In cluster Consumer Staples, the following companies are present: ['Archer-Daniels-Midland Co' 'Church & Dwight' 'Colgate-Palmolive' 'CVS Health' 'Dr Pepper Snapple Group' 'Hormel Foods Corp.' 'The Hershey Company' 'Kimberly-Clark' 'Coca Cola Company' 'Mondelez International' 'Mead Johnson' 'McCormick & Co.' 'Monster Beverage' 'Altria Group Inc' 'PepsiCo Inc.' 'Procter & Gamble' 'Philip Morris International' 'Molson Coors Brewing Company' 'Tyson Foods'] In cluster Utilities, the following companies are present: ['Ameren Corp' 'American Electric Power' 'American Water Works Company Inc' 'CMS Energy' 'CenterPoint Energy' 'Dominion Resources' 'Duke Energy' 'Consolidated Edison' "Edison Int'l" 'Eversource Energy' 'Entergy Corp.' 'Exelon Corp.' 'FirstEnergy Corp' 'Alliant Energy Corp' 'NextEra Energy' 'PG&E Corp.' 'Public Serv. Enterprise Inc.' 'Pinnacle West Capital' 'PPL Corp.' 'SCANA Corp' 'Southern Co.' 'Sempra Energy' 'Wec Energy Group Inc' 'Xcel Energy Inc'] In cluster Financials, the following companies are present: ['AFLAC Inc' 'American International Group, Inc.' 'Assurant Inc' 'Arthur J. Gallagher & Co.' 'Allstate Corp' 'Affiliated Managers Group Inc' 'Ameriprise Financial' 'Aon plc' 'American Express Co' 'Bank of America Corp' 'BB&T Corporation' 'The Bank of New York Mellon Corp.' 'Citigroup Inc.' 'Chubb Limited' 'Citizens Financial Group' 'Cincinnati Financial' 'Comerica Inc.' 'CME Group Inc.' 'Capital One Financial' 'Discover Financial Services' 'E*Trade' 'Huntington Bancshares' 'Hartford Financial Svc.Gp.' 'Invesco Ltd.' 'JPMorgan Chase & Co.' 'Leucadia National Corp.' "Moody's Corp" 'MetLife Inc.' 'Marsh & McLennan' 'M&T Bank Corp.' 'Navient' 'NASDAQ OMX Group' 'Northern Trust Corp.' "People's United Financial" 'Principal Financial Group' 'Progressive Corp.' 'PNC Financial Services' 'Prudential Financial' 'Charles Schwab Corporation' 'S&P Global, Inc.' 'SunTrust Banks' 'State Street Corp.' 'Synchrony Financial' 'Torchmark Corp.' 'The Travelers Companies Inc.' 'Unum Group' 'Wells Fargo' 'XL Capital' 'Zions Bancorp'] In cluster Real Estate, the following companies are present: ['Apartment Investment & Mgmt' 'American Tower Corp A' 'AvalonBay Communities, Inc.' 'Boston Properties' 'CBRE Group' 'Crown Castle International Corp.' 'Digital Realty Trust' 'Equinix' 'Equity Residential' 'Essex Property Trust, Inc.' 'Extra Space Storage' 'Federal Realty Investment Trust' 'General Growth Properties Inc.' 'Welltower Inc.' 'HCP Inc.' 'Host Hotels & Resorts' 'Iron Mountain Incorporated' 'Kimco Realty' 'Mid-America Apartments' 'Macerich' 'Realty Income Corporation' 'SL Green Realty' 'Simon Property Group Inc' 'UDR Inc' 'Vornado Realty Trust' 'Ventas Inc' 'Weyerhaeuser Corp.'] In cluster Materials, the following companies are present: ['Albemarle Corp' 'Ball Corp' 'CF Industries Holdings Inc' 'Du Pont (E.I.)' 'Ecolab Inc.' 'Eastman Chemical' 'Freeport-McMoran Cp & Gld' 'FMC Corporation' 'Intl Flavors & Fragrances' 'International Paper' 'LyondellBasell' 'Martin Marietta Materials' 'The Mosaic Company' 'Newmont Mining Corp. (Hldg. Co.)' 'Nucor Corp.' 'PPG Industries' 'Praxair Inc.' 'Sealed Air' 'Sherwin-Williams' 'Vulcan Materials'] In cluster Consumer Discretionary, the following companies are present: ['Amazon.com Inc' 'AutoNation Inc' 'BorgWarner' 'Carnival Corp.' 'Charter Communications' 'Chipotle Mexican Grill' 'The Walt Disney Company' 'Discovery Communications-A' 'Discovery Communications-C' 'Delphi Automotive' 'Expedia Inc.' 'Ford Motor' 'General Motors' 'Genuine Parts' 'Garmin Ltd.' 'Goodyear Tire & Rubber' 'Hasbro Inc.' 'Harley-Davidson' 'Interpublic Group' 'Lennar Corp.' 'LKQ Corporation' "Marriott Int'l." 'Mattel Inc.' "McDonald's Corp." 'Mohawk Industries' 'Newell Brands' 'Omnicom Group' "O'Reilly Automotive" 'Priceline.com Inc' 'Pulte Homes Inc.' 'Royal Caribbean Cruises Ltd' 'Scripps Networks Interactive Inc.' 'Tegna, Inc.' 'TripAdvisor' 'Tractor Supply Company' 'Under Armour' 'Whirlpool Corp.' 'Wyndham Worldwide' 'Wynn Resorts Ltd' 'Yum! Brands Inc'] In cluster Energy, the following companies are present: ['Apache Corporation' 'Anadarko Petroleum Corp' 'Baker Hughes Inc' 'Chesapeake Energy' 'Cabot Oil & Gas' 'Chevron Corp.' 'Concho Resources' 'Devon Energy Corp.' 'EOG Resources' 'EQT Corporation' 'Halliburton Co.' 'Hess Corporation' 'Kinder Morgan' 'Marathon Petroleum' 'Marathon Oil Corp.' 'Murphy Oil' 'Noble Energy Inc' 'Newfield Exploration Co' 'National Oilwell Varco Inc.' 'ONEOK' 'Occidental Petroleum' 'Phillips 66' 'Range Resources Corp.' 'Spectra Energy Corp.' 'Southwestern Energy' 'Tesoro Petroleum Co.' 'Valero Energy' 'Williams Cos.' 'Cimarex Energy' 'Exxon Mobil Corp.'] In cluster Telecommunications Services, the following companies are present: ['CenturyLink Inc' 'Frontier Communications' 'Level 3 Communications' 'AT&T Inc' 'Verizon Communications']
df.groupby(["K_means_segments", "GICS Sector"])['Security'].count()
K_means_segments GICS Sector
0 Consumer Discretionary 32
Consumer Staples 15
Energy 5
Financials 45
Health Care 29
Industrials 51
Information Technology 21
Materials 17
Real Estate 26
Telecommunications Services 2
Utilities 24
1 Consumer Discretionary 1
Consumer Staples 1
Energy 1
Financials 3
Health Care 2
Information Technology 1
Telecommunications Services 2
2 Energy 3
3 Consumer Discretionary 1
Consumer Staples 2
Financials 1
Industrials 1
4 Consumer Discretionary 5
Consumer Staples 1
Health Care 8
Information Technology 7
Materials 1
Real Estate 1
Telecommunications Services 1
5 Consumer Discretionary 1
Energy 21
Health Care 1
Industrials 1
Information Technology 4
Materials 2
Name: Security, dtype: int64
plt.figure(figsize=(20, 20))
plt.suptitle("Boxplot of numerical variables for each cluster")
for i, variable in enumerate(num_col):
plt.subplot(4, 3, i + 1)
sns.boxplot(data=df, x="K_means_segments", y=variable)
plt.tight_layout(pad=2.0)
df.groupby("K_means_segments").mean(numeric_only=True).plot.bar(figsize=(15, 6))
<Axes: xlabel='K_means_segments'>
Cluster 0:
Cluster 1:
Cluster 2:
Cluster 3:
Cluster 4:
Cluster 5:
# list of distance metrics
distance_metrics = ["euclidean", "chebyshev", "mahalanobis", "cityblock"]
# list of linkage methods
linkage_methods = ["single", "complete", "average", "weighted"]
high_cophenet_corr = 0
high_dm_lm = [0, 0]
for dm in distance_metrics:
for lm in linkage_methods:
Z = linkage(subset_scaled_df, metric=dm, method=lm)
c, coph_dists = cophenet(Z, pdist(subset_scaled_df))
print(
"Cophenetic correlation for {} distance and {} linkage is {}.".format(
dm.capitalize(), lm, c
)
)
if high_cophenet_corr < c:
high_cophenet_corr = c
high_dm_lm[0] = dm
high_dm_lm[1] = lm
Cophenetic correlation for Euclidean distance and single linkage is 0.9232271494002922. Cophenetic correlation for Euclidean distance and complete linkage is 0.7873280186580672. Cophenetic correlation for Euclidean distance and average linkage is 0.9422540609560814. Cophenetic correlation for Euclidean distance and weighted linkage is 0.8693784298129404. Cophenetic correlation for Chebyshev distance and single linkage is 0.9062538164750717. Cophenetic correlation for Chebyshev distance and complete linkage is 0.598891419111242. Cophenetic correlation for Chebyshev distance and average linkage is 0.9338265528030499. Cophenetic correlation for Chebyshev distance and weighted linkage is 0.9127355892367. Cophenetic correlation for Mahalanobis distance and single linkage is 0.9259195530524591. Cophenetic correlation for Mahalanobis distance and complete linkage is 0.7925307202850002. Cophenetic correlation for Mahalanobis distance and average linkage is 0.9247324030159737. Cophenetic correlation for Mahalanobis distance and weighted linkage is 0.8708317490180428. Cophenetic correlation for Cityblock distance and single linkage is 0.9334186366528574. Cophenetic correlation for Cityblock distance and complete linkage is 0.7375328863205818. Cophenetic correlation for Cityblock distance and average linkage is 0.9302145048594667. Cophenetic correlation for Cityblock distance and weighted linkage is 0.731045513520281.
# printing the combination of distance metric and linkage method with the highest cophenetic correlation
print(
"Highest cophenetic correlation is {}, which is obtained with {} distance and {} linkage.".format(
high_cophenet_corr, high_dm_lm[0].capitalize(), high_dm_lm[1]
)
)
Highest cophenetic correlation is 0.9422540609560814, which is obtained with Euclidean distance and average linkage.
Let's explore different linkage methods with Euclidean distance only.
# list of linkage methods
linkage_methods = ["single", "complete", "average", "centroid", "ward", "weighted"]
high_cophenet_corr = 0
high_dm_lm = [0, 0]
for lm in linkage_methods:
Z = linkage(subset_scaled_df, metric="euclidean", method=lm)
c, coph_dists = cophenet(Z, pdist(subset_scaled_df))
print("Cophenetic correlation for {} linkage is {}.".format(lm, c))
if high_cophenet_corr < c:
high_cophenet_corr = c
high_dm_lm[0] = "euclidean"
high_dm_lm[1] = lm
Cophenetic correlation for single linkage is 0.9232271494002922. Cophenetic correlation for complete linkage is 0.7873280186580672. Cophenetic correlation for average linkage is 0.9422540609560814. Cophenetic correlation for centroid linkage is 0.9314012446828154. Cophenetic correlation for ward linkage is 0.7101180299865353. Cophenetic correlation for weighted linkage is 0.8693784298129404.
# printing the combination of distance metric and linkage method with the highest cophenetic correlation
print(
"Highest cophenetic correlation is {}, which is obtained with {} linkage.".format(
high_cophenet_corr, high_dm_lm[1]
)
)
Highest cophenetic correlation is 0.9422540609560814, which is obtained with average linkage.
We see that the cophenetic correlation is maximum with Euclidean distance and average linkage.
Let's see the dendrograms for the different linkage methods.
# list of linkage methods
linkage_methods = ["single", "complete", "average", "centroid", "ward", "weighted"]
# lists to save results of cophenetic correlation calculation
compare_cols = ["Linkage", "Cophenetic Coefficient"]
compare =[]
# to create a subplot image
fig, axs = plt.subplots(len(linkage_methods), 1, figsize=(15, 30))
# We will enumerate through the list of linkage methods above
# For each linkage method, we will plot the dendrogram and calculate the cophenetic correlation
for i, method in enumerate(linkage_methods):
Z = linkage(subset_scaled_df, metric="euclidean", method=method)
dendrogram(Z, ax=axs[i])
axs[i].set_title(f"Dendrogram ({method.capitalize()} Linkage)")
coph_corr, coph_dist = cophenet(Z, pdist(subset_scaled_df))
axs[i].annotate(
f"Cophenetic\nCorrelation\n{coph_corr:0.2f}",
(0.80, 0.80),
xycoords="axes fraction",
)
HCmodel = AgglomerativeClustering(n_clusters=3, affinity="euclidean", linkage="average")
HCmodel.fit(subset_scaled_df)
AgglomerativeClustering(affinity='euclidean', linkage='average', n_clusters=3)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
AgglomerativeClustering(affinity='euclidean', linkage='average', n_clusters=3)
df1= data.copy()
subset_scaled_df["HC_Clusters"] = HCmodel.labels_
df1["HC_Clusters"] = HCmodel.labels_
cluster_profile = df1.groupby("HC_Clusters").mean(numeric_only=True)
cluster_profile["count_in_each_segments"] = (
df1.groupby("HC_Clusters")["Security"].count().values
)
cluster_profile.style.highlight_max(color="lightgreen", axis=0)
| Current Price | Price Change | Volatility | ROE | Cash Ratio | Net Cash Flow | Net Income | Earnings Per Share | Estimated Shares Outstanding | P/E Ratio | P/B Ratio | count_in_each_segments | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| HC_Clusters | ||||||||||||
| 0 | 77.653642 | 4.184271 | 1.515129 | 35.103858 | 69.798220 | 68662246.290801 | 1613508620.178041 | 2.900905 | 578930419.447478 | 32.466828 | -1.739711 | 337 |
| 1 | 1274.949951 | 3.190527 | 1.268340 | 29.000000 | 184.000000 | -1671386000.000000 | 2551360000.000000 | 50.090000 | 50935516.070000 | 25.453183 | -1.052429 | 1 |
| 2 | 24.485001 | -13.351992 | 3.482611 | 802.000000 | 51.000000 | -1292500000.000000 | -19106500000.000000 | -41.815000 | 519573983.250000 | 60.748608 | 1.565141 | 2 |
HC_Cluster 0:
HC_Cluster 1:
HC_Cluster 2:
# let's see the names of the countries in each cluster
for cl in df1["HC_Clusters"].unique():
print("In cluster {}, the following countries are present:".format(cl))
print(df1[df1["HC_Clusters"] == cl]["Security"].unique())
print()
In cluster 0, the following countries are present: ['American Airlines Group' 'AbbVie' 'Abbott Laboratories' 'Adobe Systems Inc' 'Analog Devices, Inc.' 'Archer-Daniels-Midland Co' 'Alliance Data Systems' 'Ameren Corp' 'American Electric Power' 'AFLAC Inc' 'American International Group, Inc.' 'Apartment Investment & Mgmt' 'Assurant Inc' 'Arthur J. Gallagher & Co.' 'Akamai Technologies Inc' 'Albemarle Corp' 'Alaska Air Group Inc' 'Allstate Corp' 'Allegion' 'Alexion Pharmaceuticals' 'Applied Materials Inc' 'AMETEK Inc' 'Affiliated Managers Group Inc' 'Amgen Inc' 'Ameriprise Financial' 'American Tower Corp A' 'Amazon.com Inc' 'AutoNation Inc' 'Anthem Inc.' 'Aon plc' 'Anadarko Petroleum Corp' 'Amphenol Corp' 'Arconic Inc' 'Activision Blizzard' 'AvalonBay Communities, Inc.' 'Broadcom' 'American Water Works Company Inc' 'American Express Co' 'Boeing Company' 'Bank of America Corp' 'Baxter International Inc.' 'BB&T Corporation' 'Bard (C.R.) Inc.' 'Baker Hughes Inc' 'BIOGEN IDEC Inc.' 'The Bank of New York Mellon Corp.' 'Ball Corp' 'Bristol-Myers Squibb' 'Boston Scientific' 'BorgWarner' 'Boston Properties' 'Citigroup Inc.' 'Caterpillar Inc.' 'Chubb Limited' 'CBRE Group' 'Crown Castle International Corp.' 'Carnival Corp.' 'Celgene Corp.' 'CF Industries Holdings Inc' 'Citizens Financial Group' 'Church & Dwight' 'C. H. Robinson Worldwide' 'Charter Communications' 'CIGNA Corp.' 'Cincinnati Financial' 'Colgate-Palmolive' 'Comerica Inc.' 'CME Group Inc.' 'Chipotle Mexican Grill' 'Cummins Inc.' 'CMS Energy' 'Centene Corporation' 'CenterPoint Energy' 'Capital One Financial' 'Cabot Oil & Gas' 'The Cooper Companies' 'CSX Corp.' 'CenturyLink Inc' 'Cognizant Technology Solutions' 'Citrix Systems' 'CVS Health' 'Chevron Corp.' 'Concho Resources' 'Dominion Resources' 'Delta Air Lines' 'Du Pont (E.I.)' 'Deere & Co.' 'Discover Financial Services' 'Quest Diagnostics' 'Danaher Corp.' 'The Walt Disney Company' 'Discovery Communications-A' 'Discovery Communications-C' 'Delphi Automotive' 'Digital Realty Trust' 'Dun & Bradstreet' 'Dover Corp.' 'Dr Pepper Snapple Group' 'Duke Energy' 'DaVita Inc.' 'Devon Energy Corp.' 'eBay Inc.' 'Ecolab Inc.' 'Consolidated Edison' 'Equifax Inc.' "Edison Int'l" 'Eastman Chemical' 'EOG Resources' 'Equinix' 'Equity Residential' 'EQT Corporation' 'Eversource Energy' 'Essex Property Trust, Inc.' 'E*Trade' 'Eaton Corporation' 'Entergy Corp.' 'Edwards Lifesciences' 'Exelon Corp.' "Expeditors Int'l" 'Expedia Inc.' 'Extra Space Storage' 'Ford Motor' 'Fastenal Co' 'Facebook' 'Fortune Brands Home & Security' 'Freeport-McMoran Cp & Gld' 'FirstEnergy Corp' 'Fidelity National Information Services' 'Fiserv Inc' 'FLIR Systems' 'Fluor Corp.' 'Flowserve Corporation' 'FMC Corporation' 'Federal Realty Investment Trust' 'First Solar Inc' 'Frontier Communications' 'General Dynamics' 'General Growth Properties Inc.' 'Gilead Sciences' 'Corning Inc.' 'General Motors' 'Genuine Parts' 'Garmin Ltd.' 'Goodyear Tire & Rubber' 'Grainger (W.W.) Inc.' 'Halliburton Co.' 'Hasbro Inc.' 'Huntington Bancshares' 'HCA Holdings' 'Welltower Inc.' 'HCP Inc.' 'Hess Corporation' 'Hartford Financial Svc.Gp.' 'Harley-Davidson' "Honeywell Int'l Inc." 'Hewlett Packard Enterprise' 'HP Inc.' 'Hormel Foods Corp.' 'Henry Schein' 'Host Hotels & Resorts' 'The Hershey Company' 'Humana Inc.' 'International Business Machines' 'IDEXX Laboratories' 'Intl Flavors & Fragrances' 'Intel Corp.' 'International Paper' 'Interpublic Group' 'Iron Mountain Incorporated' 'Intuitive Surgical Inc.' 'Illinois Tool Works' 'Invesco Ltd.' 'J. B. Hunt Transport Services' 'Jacobs Engineering Group' 'Juniper Networks' 'JPMorgan Chase & Co.' 'Kimco Realty' 'Kimberly-Clark' 'Kinder Morgan' 'Coca Cola Company' 'Kansas City Southern' 'Leggett & Platt' 'Lennar Corp.' 'Laboratory Corp. of America Holding' 'LKQ Corporation' 'L-3 Communications Holdings' 'Lilly (Eli) & Co.' 'Lockheed Martin Corp.' 'Alliant Energy Corp' 'Leucadia National Corp.' 'Southwest Airlines' 'Level 3 Communications' 'LyondellBasell' 'Mastercard Inc.' 'Mid-America Apartments' 'Macerich' "Marriott Int'l." 'Masco Corp.' 'Mattel Inc.' "McDonald's Corp." "Moody's Corp" 'Mondelez International' 'MetLife Inc.' 'Mohawk Industries' 'Mead Johnson' 'McCormick & Co.' 'Martin Marietta Materials' 'Marsh & McLennan' '3M Company' 'Monster Beverage' 'Altria Group Inc' 'The Mosaic Company' 'Marathon Petroleum' 'Merck & Co.' 'Marathon Oil Corp.' 'M&T Bank Corp.' 'Mettler Toledo' 'Murphy Oil' 'Mylan N.V.' 'Navient' 'Noble Energy Inc' 'NASDAQ OMX Group' 'NextEra Energy' 'Newmont Mining Corp. (Hldg. Co.)' 'Netflix Inc.' 'Newfield Exploration Co' 'Nielsen Holdings' 'National Oilwell Varco Inc.' 'Norfolk Southern Corp.' 'Northern Trust Corp.' 'Nucor Corp.' 'Newell Brands' 'Realty Income Corporation' 'ONEOK' 'Omnicom Group' "O'Reilly Automotive" 'Occidental Petroleum' "People's United Financial" 'Pitney-Bowes' 'PACCAR Inc.' 'PG&E Corp.' 'Public Serv. Enterprise Inc.' 'PepsiCo Inc.' 'Pfizer Inc.' 'Principal Financial Group' 'Procter & Gamble' 'Progressive Corp.' 'Pulte Homes Inc.' 'Philip Morris International' 'PNC Financial Services' 'Pentair Ltd.' 'Pinnacle West Capital' 'PPG Industries' 'PPL Corp.' 'Prudential Financial' 'Phillips 66' 'Quanta Services Inc.' 'Praxair Inc.' 'PayPal' 'Ryder System' 'Royal Caribbean Cruises Ltd' 'Regeneron' 'Robert Half International' 'Roper Industries' 'Range Resources Corp.' 'Republic Services Inc' 'SCANA Corp' 'Charles Schwab Corporation' 'Spectra Energy Corp.' 'Sealed Air' 'Sherwin-Williams' 'SL Green Realty' 'Scripps Networks Interactive Inc.' 'Southern Co.' 'Simon Property Group Inc' 'S&P Global, Inc.' 'Stericycle Inc' 'Sempra Energy' 'SunTrust Banks' 'State Street Corp.' 'Skyworks Solutions' 'Southwestern Energy' 'Synchrony Financial' 'Stryker Corp.' 'AT&T Inc' 'Molson Coors Brewing Company' 'Teradata Corp.' 'Tegna, Inc.' 'Torchmark Corp.' 'Thermo Fisher Scientific' 'TripAdvisor' 'The Travelers Companies Inc.' 'Tractor Supply Company' 'Tyson Foods' 'Tesoro Petroleum Co.' 'Total System Services' 'Texas Instruments' 'Under Armour' 'United Continental Holdings' 'UDR Inc' 'Universal Health Services, Inc.' 'United Health Group Inc.' 'Unum Group' 'Union Pacific' 'United Parcel Service' 'United Technologies' 'Varian Medical Systems' 'Valero Energy' 'Vulcan Materials' 'Vornado Realty Trust' 'Verisk Analytics' 'Verisign Inc.' 'Vertex Pharmaceuticals Inc' 'Ventas Inc' 'Verizon Communications' 'Waters Corporation' 'Wec Energy Group Inc' 'Wells Fargo' 'Whirlpool Corp.' 'Waste Management Inc.' 'Williams Cos.' 'Western Union Co' 'Weyerhaeuser Corp.' 'Wyndham Worldwide' 'Wynn Resorts Ltd' 'Cimarex Energy' 'Xcel Energy Inc' 'XL Capital' 'Exxon Mobil Corp.' 'Dentsply Sirona' 'Xerox Corp.' 'Xylem Inc.' 'Yahoo Inc.' 'Yum! Brands Inc' 'Zimmer Biomet Holdings' 'Zions Bancorp' 'Zoetis'] In cluster 2, the following countries are present: ['Apache Corporation' 'Chesapeake Energy'] In cluster 1, the following countries are present: ['Priceline.com Inc']
df1.groupby(["HC_Clusters", "GICS Sector"])['Security'].count()
HC_Clusters GICS Sector
0 Consumer Discretionary 39
Consumer Staples 19
Energy 28
Financials 49
Health Care 40
Industrials 53
Information Technology 33
Materials 20
Real Estate 27
Telecommunications Services 5
Utilities 24
1 Consumer Discretionary 1
2 Energy 2
Name: Security, dtype: int64
plt.figure(figsize=(20, 20))
plt.suptitle("Boxplot of numerical variables for each cluster")
for i, variable in enumerate(num_col):
plt.subplot(3, 4, i + 1)
sns.boxplot(data=df1, x="HC_Clusters", y=variable)
plt.tight_layout(pad=2.0)
df1.groupby("HC_Clusters").mean(numeric_only=True).plot.bar(figsize=(15, 6))
<Axes: xlabel='HC_Clusters'>
Which clustering technique took less time for execution?
Both Clustering took less time.
Which clustering technique gave you more distinct clusters, or are they the same?
K means clustering (silhouette) and hierarchical clustering are having same number of clusters.
How many observations are there in the similar clusters of both algorithms?
cross_tab = pd.crosstab(df['K_means_segments'], df1['HC_Clusters'])
# Display the cross-tabulation
print(cross_tab)
# Find the maximum overlap (similar clusters)
similar_clusters = cross_tab.idxmax(axis=1) # This will give you the HC cluster with the most overlap for each K-means cluster
overlap_counts = cross_tab.max(axis=1) # Number of observations in the most similar clusters
# Sum of overlaps for similar clusters
total_overlap = overlap_counts.sum()
print(f'Total number of observations in similar clusters: {total_overlap}')
HC_Clusters 0 1 2 K_means_segments 0 267 0 0 1 11 0 0 2 1 0 2 3 5 0 0 4 23 1 0 5 30 0 0 Total number of observations in similar clusters: 338
How many clusters are obtained as the appropriate number of clusters from both algorithms?
The appropriate number of clusters for both algorithms appears to be 3, as this is where the most substantial alignment occurs.